Termination has been a subject of intensive research in the logic programming community for the last two decades. Most works deal with proving universal left termination of a given class of queries, i.e. finiteness of all the possible derivations produced by a Prolog engine from any query in that class. In contrast, the study of the dual problem: nontermination w.r.t. the left selection rule i.e the existence of one query in a given class of queries which admits an infinite left derivation, has given rise to only a few papers. In this article, we study non-termination in the more general constraint logic programming framework. We rephrase our previous logic programming approach into this more abstract setting, which leads to a criterion expressed in a logical way and simpler proofs, as expected. Also, by reconsidering our previous work, we now prove that in some sense, we already had the best syntactic criterion for logic programming. Last but not least, we offer a set of correct algorithms for inferring non-termination for CLP.